ci: Refactor timelord action to use git-warp-time fallback

Updates the timelord action to fall back to git-warp-time when the cache
is completely empty, enabling timestamp restoration even on fresh builds.
Simplifies the interface by making inputs optional with sensible defaults
and adds Docker integration via buildkit-cache-dance.

docker/Dockerfile

@@ -60,6 +60,7 @@ RUN <<EOF
     curl --retry 5 -L --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/cargo-bins/cargo-binstall/main/install-from-binstall-release.sh | bash
     cargo binstall --no-confirm cargo-sbom --version $CARGO_SBOM_VERSION
     cargo binstall --no-confirm lddtree --version $LDDTREE_VERSION
+    cargo binstall --no-confirm timelord-cli@3.0.1
 EOF
 
 # Set up xx (cross-compilation scripts)
@@ -133,6 +134,14 @@ FROM toolchain AS builder
 # Get source
 COPY . .
 
+# Restore timestamps from timelord cache if available
+RUN if [ -f /root/.cache/timelord/timelord.db ]; then \
+        echo "Restoring timestamps from timelord cache"; \
+        timelord sync --source-dir /app --cache-dir /root/.cache/timelord; \
+    else \
+        echo "No timelord cache found, timestamps will be build time"; \
+    fi
+
 ARG TARGETPLATFORM
 
 # Verify environment configuration